On limit fractional Volterra hierarchies

Abstract

For the limit fractional Volterra (LFV) hierarchy, we construct the n-fold Darboux transformation and the soliton solutions. Furthermore, we extend the LFV hierarchy to the noncommutative LFV (NCLFV) hierarchy, and construct the Darboux transformation expressed by quasi determinant of the noncommutative version. Meanwhile, we establish the relationship between new and old solutions of the NCLFV hierarchy. Finally, the quasi determinant solutions of the NCLFV hierarchy are obtained.